Being an 89...maybe they kept giving you parts for the 3.0L V6 instead of the 2.6L 4cyl? All Montero's/Raider's are all the same as far as parts...the only difference between the two are the badges and some paint.
The reed valve is an air injection for the catalytic converter...it works on negative pressure exhaust pulses to draw air into the exhaust. If you have exhaust coming out of yours then it needs to be replaced. I'd get one from a junkyard to save money.
The cable is adjustable to compensate for stretch/slack. There is a bolt that holds the cable housing to the valve cover and the housing is slotted. You can loosen the bolt then gently pull the housing away from the carb to tighten up the cable action (although you want some slack so you can lower the idle speed if necessary).
If the choke is not opening, first try some spray carb cleaner and move the choke plate by hand to make sure it's able to move freely (you may need to hold the throttle open slightly in order to move the choke plate). As the engine warms it should slowly open on it's own. It can be adjusted, but that requires drilling out the three rivets on the choke assembly and replacing them with screws, then you can rotate the choke housing to increase/decrease choke spring tension.
Your whole problem could be the choke, flooring the throttle usually cracks the choke plate open, try holding it open with a big or t-handled screwdriver (so that it can't fall down into the carb) and see if it'll start to idle. Another thing to check is if the carb is dumping fuel while running. Mine did this and it looked like a waterfall of gas just running down into the primary throttle bore and when you turned off the engine you could hear it gurgling and trickling down into the engine (as well as see it by holding the choke plate open). Stuck float inside the carb was the cause.
Finally, the FSM has the best information for diagnosing the carb. There are tons of links within the forum to download them and McMontyV has a link in his sig.
